Apparatus and methods for automatic indexing and storage



March 12, 1963 H. M. SIERRA 3,081,447

APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Filed April 10, 1961 Sheets-Sheet 1 [0010205640506070809131112151415161718192021222324 34G1HSRTVF54BC2156BWC12P FIG. 1

000 (001051 J 21 50m 0/ IIIIIIHHHIIIIHIIIIII l 2 TABULATUR IDENTIFIER ADDRESS 0000 READER ADDRESS REGISTER m0 mmsmoa 5 GE'ERATOR L ADD 55 J 41 L s I Q50? CONTROL 39/ SECTION MATCH MONFFUR SIGNAL 20 R 35 as 313% v comm v as PROGRAM TRANSFER mms GATE GATE 56 34 GATE READOUT FIG 2 J INVENTOR.

STAGE HUGH M. SIERRA BY FRASER a BOGUCK/ ATTORNEYS March 12, 1963 H. M. SIERRA 3,081,447

APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE 1O Sheets-Sheet 2 Filed April 10, 1961 m OE E25 $12-2: n o x N N March 12, 1963 H. M. SIERRA 3,081,447

APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE l0 Sheets-Sheet 3 Filed April 10, 1961 March 12, 1963 H. M. SIERRA 3,081,447

APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Filed April 10, 1961 10 Sheets-Sheet 4 March 12, 1963 H. M. SIERRA APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Filed April 10. 1961 10 Sheets-Sheet 5 TABULAFED JO 1 INFORMATION FIG. 7

n ?2 n, m\ 0000mm I; ADDER MULTIPLIER 000102 2223 24 5mm B34 {1 2 P- l REGISTER /B2 dx INVERTER /M 81 x (-1) TIMING I cmcuns x fydx -!xd([ydx) dm J x m MULTI- MEMORY z ER ADDRE? x Y Y-exp(- 00 V23 Fr? March 12, 1963 H. M. SIERRA 3,081,447

APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Filed April 10, 1961 10 Sheets-Sheet 6 FIG. 8

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10 001111101 PANEL CORE 00111001 001112 11111110 01111100150 PANEL 4/ CHARACTER OUTPUT T CIRCUITS RING 025% 0500001 FIG 12 122 123 120 11 L 121 124 12s 000102000405 121222324 M A PRIMARY I 0 5 1 0 11 11 1 c 1 2 P REGSTER 011 A 1 Ag E 1 1 55110 is March 12, 1963 FIG. 9

H. M. SIERRA APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Filed April 10, 1961 10 Sheets-Sheet 7 SMQHMSQAMMHML@LiLQ i E March 12, 1963 H. M. SIERRA 3,081,447

APPARATUS AND METHODS FOR AUTOMATIC INDELXING AND STORAGE Filed April 10. 1961 10 Sheets-Sheet 8 V DICDRL ENCODING SWITCH i;

F a? TRUE ADD .m THE TRlE-COIPLEHENT m comma ADD 00am 0F me mom EEL? SIGN DECADE UN ITS DECPDE TENIHS DECADE HLNDREDTHS DECADE FIG. 10

WDUSANDTHS DECADE TEN-THOUSANDTHS DECADE HUNDRED- THOUSANDTHS DECADE March 12, 1963 APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Filed April 10, 1961 FIG. 15

G'IARMTER RING H. M. SIERRA 10 Sheets-Sheet 10 OUTPUT FROM THE ALPHA-NUMERIC DEOODER United States Patent 3 081,447 APPARATUS AND METHODS FOR AUTOMATIC INDEXING AND STORAGE Hugh M. Sierra, Santa Clara, Calif., assignor to International Business Machines Corporation, New York, N.Y., a corporation of New York Filed Apr. 10, 1961, Ser. No. 101,809 29 Claims. (Cl. 340-1725) This invention relates to equipment and methods for indexing and storing information within a computer memory and more particularly to arrangements for relating the indexing to the statistical distribution of the in formation.

In the field of data processing a computer often handles data from a wide variety of sources. Since the data is usually identified in accordance with a numbering arrangement devised at the data source, it may be expected that some translation is necessary in order to adapt the data identification arrangement to the memory address system of the computer. A first step in the data handling process is the storage of the data within the computer memory. In the usual situation, the data is in the form of information hearing items, such as punched cards, Which are to be assigned particular locations within the computer memory. Furthermore, it is desirable that this assignment be arranged so that the information bearing items may be readily retrieved when they are called for by the presentation of the item identification number. Where a relatively large number of such items are to be processed, as is usually the case, it is clearly inefiicient to require a search of the entire memory in order to retrieve an individual item; moreover, since the number of items to be processed usually exceeds the number of memory addresses which is feasible, it has been customary to compress the information by assigning a plurality of information bearing items to each discrete memory address.

In one common arrangement in data processing systems, each item identifier consists of twenty-five symbols, each of which is one of the thirty-six alpha-numeric characters, i.e., the letters A through Z and the digits through 9. Thus, there is a possibility of 36 different combinations as item identifiers. The memory within which such information items are to be stored utilizes memory addresses of five decimal digits each, thus permitting only 100,000 memory addresses. Information is retrieved by designating a memory address corresponding to a particular item identifier and then searching through the items in the designated section of the memory to find the specific item which is sought.

Obviously, it is desirable from the standpoint of efficient utilization of the memory that there be a uniform distribution of data Within the memory. In the past, the conversion of an alpha-numeric identifier to a numerical address was accomplished by a method called randomizing. This consisted of applying an arbitrary formula to the numeric portion of the identifier. This method has proven inefficient, time consuming, and relatively wasteful of memory space. Where memory space is wasted because some memory sections are incompletely filled while others overflow, it becomes necessary to pro- "ice vide additional equipment in the form of extra memory storage in order to take care of possible overflow. Thus, it can be seen that any arrangement which alfords a more uniform distribution of data. storage within a particular memory will effect savings in equipment required, time consumed in data retrieval, and cost and size of information storage equipment.

It is, therefore, an object of this invention to provide an improved arrangement for the storage of information in a computer memory.

It is a further object of this invention to provide for the uniform distribution of information items within a. computer memory.

It is an additional object of this invention to provide an arrangement for translating the identifier of an item to be stored in a memory with a maximum probability of uniform storage in the memory.

More specifically, it is an object of this invention to apply the principles of statistical analysis to the population of item identifiers in order to effect a uniform distribution of items within a memory based on the relative frequency of occurrence of the identifier characters.

It is also an object of this invention to provide for the translation of alpha-numeric identifiers to numerical memory addresses by means of equipment which is readily adaptable to handle information items of different forms from a wide variety of sources having varying arrangements of alpha-numeric identifiers.

Considered broadly, the invention contemplates the division of the memory into a number of equal portions, othewise referred to as sections or buckets, and of giving each equal portion or section of the memory an equal probability of being occupied. This is accomplished, in accordance with the invention, by dividing the total area under a Gaussian or normal distribution probability curve into equal sub-areas and assigning to each sub-area a unique memory address. This memory address is related to the frequency distribution of the set of item identifiers in a manner which minimizes variations in the distribution of items in the respective memory sections. Furthermore, the relationship between the memory address gencrating equipment of the invention and the data to be stored is readily adjustable so that the equipment may be usable, Without delay, with any set of identifiers.

Briefly, the invention involves a determination of the frequency distribution of the identifiers of a set of items which are to be stored and the operation on such information so as to convert it to a corresponding Gaussian probability curve in order that the items may be assigned to memory sections with equal probability. Initially the frequency distribution of the set of data which is to be processed is determined by sorting and tabulating the information bearing items according to the particular alphanumeric character occurring in a given identifier position. In the event that the set consists of a very large number of information items, an estimate of the frequency distribution may be made by sorting and tabulating the items in a statistical sample of the complete set. The list of alpha-numeric characters for the selected identifier position is then ordered by beginning with the most frequent character and alternately ranging on opposite sides thereof the succeeding characters taken in the order of their respective frequencies of occurrence. If viewed on a graph as a plot of frequency of occurrence versus character, the result is a histogram having a peak in the center and receding on both sides. Each alpha-numeric character is then given a rank number beginning at one end of the histogram and continuing sequentially to the other end. Each frequency of occurrence number is transformed to a relative frequency of occurrence by taking the ratio of the particular number to the total number of items being processed. From these values a cumulative distribution function is obtained which for any rank consists of the sum of the relative frequency of occurrence values of all the ranks preceding it.

For a reason which will be explained below, the entire list of cumulative frequencies thus obtained is shifted slightly by deriving a series of midpoint cumulative frequencies as averages of each pair of adjacent cumulative frequency values. Once this list is derived, it is a simple matter to go from a list of cumulative frequencies to the corresponding Gaussian probabilities of occurrence by means of published statistical tables. Such a table, for example, appears at page 229 et seq. of the Hand book of Chemistry and Physics, thirty-fourth edition. From such a table a list of corresponding T values, or normal deviates, corresponding to the midpoint cumulative frequencies may be obtained. Similar information is derived for the frequency distribution of the characters in each identifier position so that in the case of identifiers utilizing twenty-five positions or digits there will be providcd twenty-five lists of normal deviate values and twenty-five rankings of the alpha-numeric characters employed. The above described operations are commonly performed by the user prior to the presentation of the information which is to be processed in the computer. It may if desired, however, be performed as a first step of the data processing procedure.

Once the above information is applied to the memory addressing section of the computer, the system is ready to begin storing (or retrieving) the respective information items. As each item is presented its identifier is analyzed, character by character, in accordance with the above described statistical analysis of the item set. By appropriate operations corresponding to the mathematical steps described above, the structure of the invention automatically generates a memory address which corresponds to the particular identifier being examined and which is related statistically to the frequency distribution of the entire set. Thus, each section of the memory is caused to have an equal probability of occupancy for the respective items of the set so that the information is uniformly distributed over the memory with a minimum occurrence of overflow from any of the individual sections and a corresponding reduction in the additional equipment which must be provided to take care of memory overflow.

A better understanding of the invention may be had from a consideration of the following detailed description taken in conjunction with the drawings, in which:

FIG. 1 is a representation of a typical item in the form of an accounting card bearing information to be stored in a computer memory associated with the invention;

FIG. 2 is a block diagram representing a system in accordance with the invention;

FIG. 3 is a plot of an arrangement of data at one stage in the practice of the invention;

FIG. 4 is a graph of data derived from the information presented in FIG. 3;

FIG. 5 is a graph of the Gaussian distribution curve corresponding to the graph of FIG. 4;

FIG. 6 is a graph which is useful in the explanation of the operation of the invention;

FIG. 7 is a block diagram depicting in greater detail a. portion of the system of FIG. 2;

FIG. 8 is a schematic diagram representing a portion of the structure of the invention as depicted in the block diagram of FIG. 7;

FIG. 9 is a detailed schematic representation of another portion of the invention as depicted in FIG. 7;

FIG. 10 is a schematic representation of an arrangement which may be employed in the circuit of FIG. 8;

FIG. 11 is a diagram of a portion of a control panel suitable for use with the arrangement of FIG. 8;

FIG. 12 is a more detailed representation of a portion of the arrangement of FIG. 7;

FIG. 13 is a schematic representation of one segment of the block diagram of FIG. 12;

FIG. 14 is a schematic representation of a second segment of the block diagram of FIG. 12;

FIG. 15 is a schematic representation of a third segment of the block diagram of FIG. 12;

FIG. 16 is a block diagram embodying a modification of the arrangement depicted in FIG. 7; and

FIG. 17 is a more detailed schematic representation of portions of FIGS. 14 and 15.

Before beginning the detailed description of the in- Mention it may be useful to review certain well-known principles of probability and statistics in order to provide a better understanding of the operation of the invention. These statistical principles and nomenclature may be found in almost any textbook on statistics, one such textbook being Statistical Theory With Engineen ing Applications" by A. Hald.

The probability that a stochastic variable x will take on a value less than or equal to a specified number 1c is written P{xx This probability, which is a function of x,,, will be written more briefly as P{x,,}; i.e.:

Usually the stochastic variable and the actual variable x are denoted by the same letter if no confusion is likely. Pix is called the cumulative distribution function of the variable.

The probability that the stochastic variable x takes on a value in the interval x xx is written.

The cumulative distribution funntion may be considered the successive addition of the individual values of a variable over the range of the variable. For a continuous variable t, normally distributed, the standardized cumulative distribution function may be represented by the expression where exp represents the base 0 of the natural system of logarithms talcen to the exponent indicated in parentheses, in this case The corresponding standardized normal distribution function, which is also referred to as the Gaussian curve, may be represented as It can be seen that Equation 2 is the integral of Equation 3 between specified limits and that any particular value of the standardized cumulative distribution curve represents the area to the left of the corresponding ordinate of the standardized Gaussian curve. An example of a standardized cumulative distribution curve may be found in FIG. 4 and the corresponding Gaussian curve may be found in FIG. 5.

The normal, or Gaussian, distribution function which is a particular case of a continuous distribution is defined by where 5 is the mean or average value of the variable and ois the standard deviation about the mean, the square of the standard deviation, is called the variance and is often preferred as a parameter of the distribution in place of the standard deviation. For the Gaussian distribution function the probability that the variable is less than or equal to t becomes By introducing a new variable the standardized normal distribution function {u} of Equation 3 is obtained from Equation 4. Similarly, the standardized cumulative distribution function Mu} of Equation 2 may be obtained from Equation by such a change of variable. For the standardized normal distribution function, the mean 5:0 and the variance (7 :1. The standardized normal distribution is symmetrical about the value of the variable equal to zero, and the entire curve representing the function over the extent of its range has an area of unity. Thus, the corresponding standardized cumulative distribution ranges from 0 to 1. By substituting D and 1 for .5 and a respectively in Equations 5 and 4 it can be seen that these equations simplify to the standardized cumulative distribution function of Equation 2 and the standardized normal distribution function of Equation 3 respectively as shown above.

With this brief background, a detailed description of the invention will now be undertaken. The invention will be discussed in terms of a preferred embodiment which utilizes a particular type of magnetic storage memory comprising a plurality of magnetizable discs each having a plurality of information tracks thereon. It should be clearly understood, however, that the aspects of the invention relating to the automatic generation of memory addresses may be employed in other information storage systems utilizing various other types of memory structures. Accordingly, the scope of the invention is not intended to be limited by the particular memory structure which is described herein.

Furthermore, for simplicity, the description of the invention will be in the context of a system wherein information is initially presented usually in the form of holes in a series of stiff paper cards, commonly referred to as punched cards. Therefore, the invention can be thought of as providing a discrete memory address or index for each card of a set which is to be processed, thus permitting the information from an entire set of cards to be stored in the memory, once the information has been read off the cards and translated to a form which is suitable for storage in the associated memory. In accordance with the invention, information from the respective cards of the set is stored in particular locations of the memory which are related to the statistical distribution of the card identifiers so that each memory section has an equal probability of being filled. Storage in this manner facilitates the retrieval process considerably, since the information from a particular card may be retrieved from the memory by obtaining its memory address from the memory address generator upon presentation of the card identifier thereto in the same way that the address was generated upon storage, and then searching through the designated memory section until the information bearing the particular card identifier is located. By relating the memory addresses to the statistical distribution of the card identifiers in a particular set of cards, as will be described in accordance with the invention, storage in the memory is effected with a minimum of overflow from individual memory sections, the requisite translating equipment for locating the information corresponding to a particular identifier in the memory is simplified, and the storage apparatus is advantageously rendered readily adaptable for use with any set of information items while maintaining a maximum efficiency of storage.

Although the invention will be described in the above mentioned context, it should be clearly understood that its utility is not restricted thereto. The invention is equally applicable to the processing of information presented in a wide variety of forms, as for example, paper tapes, magnetic tapes, magnetically printed media and even information obtained directly from an operators keyboard, so long as the tabulation of a statistical analysis of the presented information, or a suitable sample thereof, is available. All that is needed to adapt the invention to the processing of information presented in any medium is the provision of an information reader which can serve to translate the information from the presented medium to a form suitable for storage in the associated memory.

Referring now to the drawings, FIG. 1 represents a typical information bearing item 10, such as a punched card, which may be presented for storage within the memory unit of the system of the invention. The card 10 is shown bearing a representative alphanumeric identi tier 11 comprising twenty-five characters drawn from the set of twenty-six alphabetical letters and ten numerical digits. The twenty-five identifier positions are shown numbered from 00 to 24 and the respective characters shown therein are merely representative of a particular identifier which may correspond, for example, to a catalog part number, a name, an automobile engine number, or other information.

FIG. 2 is a simplified block diagram representative of an information storage system in accordance with the invention. In FIG. 2 a memory address generator 23 is shown connected to an address register 27 which is arranged to control the position of a transducer arm 26 adjacent a disc storage memory unit 28. The memory address generator 23 receives data relating to the statistical analysis of a set of information items 20 from a tabulator 22 which is connected to a card sorter 21. The memory address generator 23 also receives information relating to a specific identifier from either a card reader and translator 25 or a computer program stage 38, both of which are responsive to a control stage 40.

The output of the memory address generator 23 is applied to the address register 27 and also to an address match stage 42 which controls a first transfer gate 30. A section monitor stage 33 controls a second transfer gate 32 which is connected to the first transfer gate 39. The transfer gate 32 is alternatively controlled by the output of a gate 35 which receives signals from an identifier match stage 34 and is itself responsive to the control stage 40. The identifier match stage 34 is connected to compare signals from the computer program stage 38 and the transfer gate 32 in order to control an output gate 36 which, when activated, applies information from the disc storage memory unit 28 to a read out line which serves as the output of the system. The tabulator 22 and the memory address generator 23 are shown connected by a dashed line in order to indicate that the statistical data from the tabulator 22 is presented at a different time from that at which the identifier is presented from either the card reader and translator or the computer program stage 38.

In the operation of the system of FIG. 2, the information items 20 are directed to a sorter 21 which sorts all of the information items according to the alpha-numeric character which is found in a particular identifier position. Depending upon the number of information items that comprise a set which is to be stored in the mcrnor they may all be run through the sorter 21 or alternutivciy, a statistical sample of the set of information items may be sorted to serve as a basis for an estimate of the distribution of the entire set. After the cards 2i) are sorted, they are run through a tabulation 22 which provides, as its output, data relative to the number of cards bearing the different alpha-numeric characters. This data from the tabulator 22 may be ocnsidered a series of frequency distributions for the respective identifier positions taken with respect to alpha-numerie character. This data is then presented to the memory address generator 23, which will be described in detail below, in order that an appropriate memory address may be provided when desired.

Once the data received from the tabulator 22 is stored within the memory address generator 23 in the form of statistical parameters derived from tabulated statistical distributions, the system is ready for the second phase of operation which relates to the direct storage and retrieval of information, such as may be contained on an individual card 10, within the disc storage memory unit 28 itself. The storage unit 23 is represented as a plurality of magnetizable discs which are adapted to store input information in particular locations thereon. In a preferred arrangement the storage unit 28 may comprise one hundred metallic discs coated on each side with a ferrous oxide material well known in the art as a suitable magnetic recording medium. Each side of each disc is arranged with one hundred concentric magnetic recording tracks, so that there are ZtLODO such tracks in all. and each track is divided into five sectors or sections. Thus the memory unit 28 possesses a capacity of 100,000 sections, each of which will accommodate the storage of one hundred eight bit characters.

A five-digit file address, generated by the memory address generator 23, is utilized to select a given section to be read from or recorded into. Four of the five digits are used to control the address register 27 which is the access mechanism that positions the transducers associated with the arm 26 adjacent the desired track of the selected dis The remaining digit controls the selection of the appro priate memory bucket. The discs are numbered 00 through 99 and are addressed by similar numbers. The tracks are identified by numbers 00 through 99, each number referring to corresponding tracks on both sides of a disc. Thus, each track includes ten records, i.e., five on each side of a disc, which are referred to and are addressed by the numbers 9 through 9. In the system of FIG. 2, the first four digits of the address from the memory ,"cnerator are employed by the address register 27 to position the arm 26 While the remaining digit is utilized by the address match stage 42 to provide a selection of the address section. The first two digits of the memory address, therefore, control the address register 27 to position the transducer arm 26 opposite a selected disc. The next two digits of the memory address control the address register 27 to position the transducers of the arm 26 opposite the selected track of the selected disc. The last digit of the memory address controls which of the two transducers is selected for operation as Well as causing a selection of the specific section by means of the address match stage 42.

With regard to the description of the address control and memory portion of the system of FIG. 2 contained in the previous paragraph, the operation thereof is identical, regardless of whether information is to be stored in or retrieved from the memory unit 23. The same is true with respect to the operation of the memory address generator 23 which will be covered in detail in connection with the description of FIG. 7. The operation of the system of FIG. 2 will now be described as it provides for the storage of a particular information item in the memory unit 28, to be followed by a description of the operation of the system during the retrieval of a particular information item from the memory unit 28.

Let it be assumed that the control stage 40 of FIG. 2 is set to effect the storage of information in the memory unit 28. A particular card 10 is applied to the card reader and translator 25 which ascertains the card identifier and applies it to the memory address generator 23. As has already been mentioned, the data relating to the statistical analysis of the particular set of information from which the card It} is drawn has previously been presented by the tabulator 22 and stored Within the memory address generator 23 in the form of a plurality of normal deviate values corresponding to character rank. Upon presentation of the identifier from the card reader and translator 25, the memory address generator 23 proceeds to operate upon the previously stored data in order to generate a corresponding five-digit memory address. As previously described, this address causes the address register 27 to position the transducers attached to the arm 26 opposite the particular track containing the section within which the information from the specific card it} is to be stored.

It will be understood, of course, that the discs of the memory unit 28 are rotating constantly so that all five sections in the selected track pass under the appropriate transducer of the arm 26 in succession. These transducers are such that they record upon the magnetic track when energized and read therefrom when not energized. It may be mentioned that the transfer gates 30 and 32 are represented as providing a connection between the right hand terminal and the lower of the left hand terminals in the absence of a control signal applied to the gate. It will, therefore, be clear that signals previously recorded on the selected track of the memory unit 23 are read out and applied via the first transfer gate 30 as one input of the address match stage 42. These signals represent information of three types: namely, signals which serve to designote the particular sections of the track, signals which correspond to the identifier of a particular information item stored in the section, and signals which represent the information that has been transferred to the selected section of the memory unit 28 from an individual information item 10.

As these various signals are directed to the stage 42, they are compared with a representation of the section selection digit of the five-digit address provided by the memory address generator 23. When a match is detected, signifying that the transducer has reached the designated memory section, a match signal is applied from the address match stage 4-2 to the transfer gate 30 which serves to transfer the connection within the gate 30 to the upper left hand terminal thereof. The signals are then applied by means of the transducers on the arm 26 from the selected storage track through the transfer gate 30 via the upper left hand terminal thereof, thence through the transfer gate 32 to the lead connected to the lower left hand terminal of the gate 32.

A particular information item may represent information not yet stored in the storage unit 28 or it may call for a change in information previously stored therein as, for example, when a particular record of an inventory item is to be changed from a corresponding record for a previous period. If the information is to be initially stored, an empty space within a memory section must be located; while if previously stored information is to be changed, the position where that information is presently stored must be located so that the new information may be recorded over the previously stored record. For purposes of illustration, assume first that an information item is to be initially stored. As the transducer of the arm 26 passes adjacent information which may be already stored in the selected section of the memory unit 28, signals from the transducer are fed to the section monitor 33 which listens for an empty portion which may be available for storage within a designated section. When such a portion is reached by the transducer, the signals from the transducer on the arm 26 are terminated; and the section monitor 33 responds by applying a transfer signal to the transfer gate 32, shifting the connection within the gate 32 to the upper left hand terminal thereof, and simultaneously applying a signal via the lead 39 to the card reader and translator 25. Upon receipt of the signal from the section monitor 33, the card reader and translator proceeds to apply signals representative first of the card identifier and then of the information contained on the specific card 10' over the lead 31 connected to the upper left hand terminal of the transfer gate 32 through the transfer gates 32 and 3t and thence to actuate the transducer on the arm 26 in order to store these signals within the storage region of the addressed section of the memory unit 28. During this step the gate and the stage 34 perform no function because there is no requirement for an identifier comparison.

When the card 10 carries information to be recorded in place of already stored information, however, the identifier from the card reader and translator 25 is applied to the identifier match stage 34 in addition to the memory address generator 23. The locating and monitoring of the addressed section proceeds in the manner described above. Now, however, there is a match between the item 10 identifier and one of the item identifiers stored in the section. When the signals read out and applied to the identifier match stage 34 match the corresponding signals from the card reader and translator 25, the stage 34 sends a signal via the gate 35 (previously enabled by a store signal from the control stage to the lead 41. This signal on the lead 41 is applied to the transfer gate 32 to switch its connection to the upper left hand terminal thereof in preparation for receiving stored signals on the lead 31. The lead 41 also applies the signal to the card reader and translator 2S, directing it to store the new information from the particular card it) (without the identifier) in the appropriate section location. When the information has been thus stored within the selected memory section, the system is ready to store information from another card It) or may be utilized to retrieve information from sections within the memory unit 28.

To retrieve information from a particular storage section within the memory unit 28 of FIG. 2, the control stage 40 is set to apply a retrieve signal to the computer program stage 33. This causes the latter to apply a speciiic identifier, corresponding to the particular information which is to be retrieved, to the memory address generator 23 and also to the identifier match stage 34. The memory address generator 23 thereupon provides a corresponding section address in the same manner in which it operates during the storage phase. The generated section address thereafter causes the address register 27 to control the arm 26 so as to position the associated transducers adjacent the appropriate track of the particular disc within the memory unit 28. The signals recorded on this track are then read out and passed through the transfer gate 30 via the lower left hand terminal thereof and thence to the address match stage 42. When a match is detected therein, signifying that the transducer has reached the particular section corresponding to the gem crated address, a match signal from the stage 42 applied to the transfer gate 30 causes a connection to be made between the transducer and the upper left hand terminal of the gate 30 which is conected to the transfer gate 32. As before, the signals generated by the transducer in correspondence with the information carried on the selected track within the selected memory section are directed to the lower left hand terminal of the transfer gate 32. At this time the function of the section monitor 33 is of no consequence. The read out signals are applied to the identifier match stage 34 and to the input of the gate 36 controlled thereby. When the identifier match stage 34 detects a match between the signals received from the memory unit 28 and the particular identifier signals receivcd from the computer program 38, an energizing signal is directed to the gate 36 which permits it to pass the signals from the memory unit 28 to the read out line connected at its output.

By means of the operation just described the system of FIG. 2 generates a particular memory address corresponding to a submitted identifier. If this identifier is received from the card reader and translator 25, signifying that information is to be stored within the memory, the address is used to select a particular section or segment of the memory, which is then monitored until the appropriate storage area is located therein after which the information to be stored is transmitted to the magnetic storing transducer. If the particular identifier is applied from a computer program, signifying that information within a corresponding section of the memory is to be retrieved, the address is similarly utilized as in the storage process to select the appropriate section within the memory unit 28. Thereafter, the information already stored within this section is monitored until a match is detected between identifier signals from the section and signals representative of the selecting identifier. The information corresponding to the appropriate identifier is then read out of the memory unit 23 and applied as an output of the system.

The memory address corresponding to any particular item identifier from the entire set of information items may be developed in accordance with the invention by the practice of the following method and by means of the structure which is hereinafter described for practicing this method. As already described above, the statistical data relating to a particular set of informaiton items, i.e., the frequency distributions with respect to alpha-numeric character for the respective identifier positions, is received by the memory address generator 23 of FIG. 2 from the tabulator 22. This data is first employed to develop, a particular ordering of the alpha-numeric characters in a manner which may best be understood by reference to FIG. 3, which is a histogram of the frequency of occurrence with respect to alpha-numeric character for the characters found in position 03 of a specific set of cards which may be employed as an example. The histogram of FIG. 3 is prepared by placing the most numerous character in the center and then proceeding in both directions therefrom in the order of frequency of occurrence, alternately ranging the characters first on one side and then on the other side of the most numerous character. Finally a numerical rank from I to 36 is assigned to each of the alpha-numeric characters in the order in which they are found in the histogram of FIG. 3. From the information received from the tabulator 22 and arranged in the manner just described, the following Table I may be prepared:

equal to infinity. To avoid this problem in statistical analysis the obtained values are shifted slightly. This TABLE I Table for Identifier Posmon 03 Num- Gumu- Cumula- Midpoint Rank Char. her of lative tive Fcn+ Cumula- Cards Number Frequency I tn-l) tive Ni, F Frequency 1838 1,838 0. 017553 0. 017553 0.008777 1931 3, 709 0. 035994 0. 053547 0. 020774 2081 5, 850 0. 055803 0. 091802 0. 0 15931 2220 S, (176 0.077127 0. 132995 0. (1100493 2303 10, 379 0. 099120 0. 170247 0. 088124 2381 12, 700 0.121859 0. 220979 0.110189 2530 15, 290 0. 146021 0. 207880 0. 2796 18. 086 0. 172723 0. 3187-14 0. 2875 20. 901 0.200179 0. 372902 0. 2902 23. 923 0. 228457 0 428616 0. 3088 27. 011 0. 257958 0 480 125 0. 3209 30,220 0. 288604 0 546562 0. 3287 33. 507 0. 319995 0 608509 (1. 3362 36. 369 0. 352102 0 672097 0. 3092 40.471 0. 386502 0 738604 0.. 3861 41. 3%2 0. 423375 0 809877 0.- 4134 13.406 0. 462855 0. 880230 0. 4058 53.121 0. 507339 0. 7 (J. 4221 57, 345 0. 517650 1. 0. 3982 01, 327 0. 585079 1. 0. 3710 05,057 0.621390 1. 0. 3111 68,478 01353971 1. 0. 3330 71.503 0.685773 1. 0. 3213 75.051 0.710714 1. 0. 3174 73. 225 0. 717050 1. 0. 3071 81, 291i 0. 770395 U. 2891 84, 181 08039111 1. 0. 2854 87,041 0 831250 1. 0. 2780 89, 821 0 057799 1. 0. 2163 02, 284 0 801321 1. 0. 2347 94,631 0 903735 1. 0. 2258 90,889 0. 925299 1. 0. 2132 99,021 0. 945660 1.8 0. 2067 101,088 0. 905400 1. 0. t 1801 102, 049 0. 983173 1.. 0. 1762 104 711 1.000000 1. 0. 991587 t of!) (From (From the the table) table) 2 38 0. 023 -1 93 0.062 1 08 0.097 1 51 0.128 1.35 0. 100 123 0. 187 l. 11 0. 210 -1. 00 0. 242 0. 89 0. 269 0 79 0.292 0 70 0.312 0 b0 0. 333 0 51 0.350 0. 42 0. 305 0. 33 0. 378 0. 24 0. 388 0. l4 0. 395 0. 04 0. 3930 0. 07 0. 398 0. 17 0. 393 0. 26 0. 380 0. 35 0. 375 (J. 4 1 0. 302 0. 53 0. 3 17 0. 2 0. 329 U. 71 0. 310 0.81 (1. 287 0.91 0. 264 1.01 0. 239 1. 12 0. 213 1. 2 0.185 1. 37 0. 150 1. 52 0. 126 1.70 0.094 1. 95 0.059 2. 39 0.023

In the data shown in Table I an actual sample of 104,711 cards was employed. This number is far below the capacity of the computer memory but will serve to illustrate particular principles employed in the practice of the invention. The card identifiers have twenty-five identifier positions. Each identifier is to be transformed in accordance with the invention to a five-digit memory address number so that each memory section has an equal probability of being filled as the information items are stored in the memory.

In Table I, the first column indicates the rank of the corresponding character of column number 2 as developed from the ordering of the tabulated data in the manner described in connection with FIG. 3. Column 3 lists the corresponding frequency of occurrence for the respective alpha-numeric characters. Column 4 lists the cumulative number N and is derived by adding for each rank the corresponding number of cards from column 3 to the preceding cumulative number in column 4. For rank 1 the cumulative number equals the number of cards for this rank which is 1838 in this case. For rank 2 the cumulative number N is equal to the number of cards for rank 2, 1931, added to the previous cumulative number, 1838, for a total of 3769. The remaining cumulative numbers are derived in similar fashion with the cumulative number corresponding to rank 36 being equal to the total number N of cards employed in the sample.

The numbers of column 4 are then transformed to cumulative frequency values F found in column 5 by dividing each corresponding number N by the total number of cards N, which is 104,711 in this example. Notice that for the last rank, since the cumulative number is N, the cumulative frequency is This presents a problem because for the cumulative frequency 3L(I)==1, derived from Equation 2 above, I is is accomplished by obtaining an intermediate cumulative frequency which is a midpoint frequency between the frequency under consideration and the one immediately preceding. The process involves obtaining an average of two adjacent cumulative frequencies and is done by adding the values of each pair of adjacent cumulative frequencies and dividing the result by two. Column 6 lists the corresponding sums of each pair of adjacent cumulative frequencies F found in column 5 and is represented by the function F -l-F F represents the cumulative frequency of the rank under consideration while F represents the cumulative frequency of the rank previous to the one under consideration. For rank 1 there is no preceding rank so the value of F -I-O is obtained. For ranl; 2 the value in column 6 corresponds to the sum of P for rank 2 plus F for rank 1 and so on.

Each value found in column 7 which is a corresponding midpoint cumulative frequency is simply the sum found in column 6 for that rank divided by 2. In other words, the values in column 7 are only half of the corresponding values in column 6. These midpoint cumulative frequencies are the values which are used for the 0(2) functions derived in accordance with Equation 2.

The values in column 8 are derived from the corresponding values of the midpoint cumulative frequency found in column 7 by referring to a statistical table of tl/(t) such as may be found, for example, in Tables of Probability Functions, vol. II, by Arnold N. Lowan.

FIG. 4 is a plot of a normalized cumulative distribution function for a continuous variable upon which the data of columns 1, 7 and 8 of Table I have been superimposed. The individual points plotted along the smooth curve correspond to the midpoint cumulative frequencies of column 7 from the table and are plotted with respect to the corresponding r values shown in column 8. The plotted points are further designated by the corresponding rank as listed in column 1.

Once the r values of column 8 are established, the correspending (t) values defined by Equation 3 above may be entered in column 9 from the same statistical table from which the values of tin column 8 were taken. A plot of the values listed in column 9 may be found in FIG. 5 which is a plot of the standardized Gaussian distribution function upon which the discrete values of (t) listed in column 9 of Table I have been superimposed.

The graphs of FIGS. 3 and 5 may now be compared. Although the coordinate scales of both figures are entirely different, the similarity between their shapes is readily apparent. The histogram of FIG. 3 has been converted into the Gaussian curve of FIG. 5. This conversion has a dual purpose: to help in filling the system memory uniformly; and to obtain t values (normal deviates) which will be useful for further analysis.

The Gaussian distribution curve of FIG. 5 represents the probability density for a particular variable taken over the range of the variable. Thus, given a particular range of the variable centered about a selected normal deviate value (I), the probability that the variable will fall within the limits of this range can be readily determined; in fact the probability is proportional to the area circumscribed by the intersected portions of the curve and the base line and by the limits of the range. Or, considered another way, the limits of the range can readily be determined when a selected normal deviate value and a given probability of occurrence are specified.

It has already been stated above that the data contained in Tablel and the standardized normal cumulative distri bution curve of FIG. 4 relate to the frequency of occurrence of the respective alpha-numeric characters for only one of the twenty-five identifier positions, in this case, position 03. Furthermore, it has been stated that similar information is provided for each one of the twenty-five identifier positions. The next step is to combine the statistical information for all of the identifier positions in order to obtain a uniform memory distribution. In order to explain the way in which this combination can be obtained resort will be had to principles of the theory of probability and the properties of the cumulative distribution function.

A proof of the Addition Theorem for a normal distribution can be found in many textbooks on statistics, e.g., Statistical Theory With Engineering Applications, by A. Hald, pages 214 to 216. This theorem states:

If the variables x x x .r are stochastically independent and normally distributed with parameters (51 '1 (52, '2 5s, 3 (En: 11

the variable XZG1XI+OI2X2+IX3XH+ will then be normally distributed with parameters (:3, c given by where n equals the number of identifier positions contributing the memory address (n 25), then Equation 7 becomes the arithmetic average of the variables x x x x Similarly, Equation 8 becomes the arithmetic average of the means 5 5,, of the respective individual distributions. Equation 9 becomes times the average variance of the variable.

14 For each one of the twenty-five identifier positions there is a standardized normal cumulative distribution curve; i.e.;

In that case, a (x):1 and the variance of the arithmetic mean will be resulting in the relationship that the standard deviation of the arithmetic mean atE) is equal to The above is summarized in another theorem which states that the standard deviation of the arithmetic mean, also known as the standard error of the arithmetic mean, is equal to times the standard deviation of the observations and no other estimate of 5 exists with a smaller standard error. As applied to the present situation this statement implies that the probability of error may be diminished, and indeed may be minimized, by resort to the frequency of occurrence distribution for all of the twenty-five identifier positions rather than by mere reliance upon the frequency of occurrence distribution for only one position. Even though there may not be expected any great variations in the parameters of the distributions for different identifier positions, what happens when a number of such distributions are combined is that the errors occurring in one distribution tend to be compensated for by similar errors in another distribution, so that all of these errors tend to cancel each other when the Addition Theorem is employed.

Furthermore, it must be understood that in many cases the data submitted from a particular source, e.g., a computer customer, is not permanently static. For example, oftentimes the data may refer to a manufacturers inventory, in which case as new part numbers are added and obsolete ones deleted the parameters of the twenty-five normal distributions may be expected to change. By taking all of the twenty-five individual distributions into account, however, the errors occurring from reconsideration of the frequency of occurrence distribution for only one identifier position and also the changes in the part numbers due to deletions and accretions tend to cancel each other out when all of the distributions are combined into one composition of data. Thus the resultant error obtained is the theoretical minimum and the reason for using all of the twenty-five normal distribution curves is to minimize the expected error.

By applying the above stated Addition Theorem, we may obtain the standard deviation of the arithmetic mean for any particular item identifier which may be presented. For example, suppose that the item 10 of FIG. 1 having the identifier 11 is presented in order that the corresponding memory address may be derived. This identifier 11 has the letter G in the identifier position 03. From columns 2 and 8 of Table I, which has already been stated to be a treatment of the distribution of alpha-numeric characters found in the identifier position 03, it can be seen that the character G (rank 35) has a 2 value of 1.95. It has already been indicated that similar tables are prepared for each of the twenty-five identifier positions. Thus for each alpha-numeric character in the identifier 11 of FIG. 1, there exists a particular 2 value which is available by reference to the appropriate table. Suppose that from the table for identifier position 00, it is found that the alphanumeric character B carries a corresponding 1 value 1 equal to 0.24. Similarly, suppose that from the table for identifier position 01, it is determined that the character 3 carries a a value equal to 1.15. In a similar fashion the appropriate t values for all twenty-five positions may be obtained; let it be assumed that they correspond to the values listed in the following Table II:

We now use this information in resorting to the statement derived above in connection with the Addition Theorem, Equations 10 and It, that the standard deviation of the arithmetic mean is equal to times the standard deviation of the observations. Thus We are able to obtain the standard deviation of the arithmetic mean for the t values listed in Table II, WillCll will be designated d The time has now arrived to apply an inverse transformation in order to compute the memory address corresponding to a particular information item identifier. Reference is made to FIG. 6 which depicts a standardized Gaussian or normal distribution curve, corresponding to the function of Equation 3 represented as a distribution of the variable d. The probability that a stochastic variable d will take on a value between two given numbers d and d is represented in FIG. 6 by the area enclosed by the curve, the d axis, and the ordinates through 11 and d as shown by the shaded portion. This area is equal to and as a result of the Addition Theorem We have for p-{d} the Gaussian curve Let us assume that the memory under consideration has 100,000 individual sections in which information items are to be segregated. Each section is designated and retrieved by a five-digit number (00000 to 99999) which is the section address. Each of the 100,000 numbers determines a well defined portion of the memory. Since all portions are equal, it is desired to give to each one an equal opportunity or an equal probability of being filled. Since the probability is given by the area under the Gaussian distribution curve, the entire area under the Gaussian curve can be divided into 100,000 equal subareas and to each of these sub-areas one of the numbers from 00000 to 99999 can be assigned corresponding to the section address.

It has been demonstrated that the area under the Gaussian curve of FIG. 6 is given by Equation 15. Since it is common in tables of statistical data to use minus infinity as the lower limit of integration, Equation 15 can be modified thus:

d, -J e.rp(- )dd 'W'Zn' 2 It now remains to choose the limits d and d so as to divide the area into 100,000 equal sub-areas. By labeling the sub-areas with numbers from 00000 to 99999 a list, of which the following Table ill is representative, is obtained:

TABLE III Table 0] Limits of Sub-Areas and Corresponding Section Addresses (la 2 db z SLCtlOn crp dd crp d1! Address \211' "llwr 000000000. 0. 000000900. 00000 0.0000000. 0000010000. 00001 0. 00002000. 00001120099. 00002 0.00003000. 0000030009. 00003 0. 00001000 01100010990. 01001 000005000. 0. 00005 1. 00005 0. 0.00101 0. (r1000 0.: 0000170 00007 0.0:s001. 0. 000050900 0000s 0. 00000010. 0. 001' 0900. 01000 000010000. 0. 1100000. 00010 000011001). 0000119909 00011 0. 98071000. 0... 08071 0. 90072000. t 0s072 0.0s073000. 0.. 93073 0.0s071000. 0.; 05074 0.. t .1000. 0. 1 9.5075 0. 0. 03076 0. 0. 98077 0.. 1 t 0. 17 00075 0.08 .0000. 0. 00170009. 03079 0051050000. 0. 050800099. 951000 0. 00002000 0. 000020009. 99092 0.. 0. 909030099. 90003 0. L 0. 000040099 9999i 0 u 0. 9090500210. 09995 0. 0. 999000999. 99005 0. 0.= 999. 09907 0. 0. 090001909. 0090s 0. 0090300999 90909 A revision of Table III shows a significant fact: the section address is given by the first five decimal digits of either integral or by any value between these two limits. In other words, the entire area of the Gaussian curve has been divided into 100.000 equal sub-areas and in Table III there are supplied in columns 1 and 2 thereof the upper and lower limits respectively of these subareas. By the use of Formula 15 or 16 any value of dzd has an equal probability of falling between the values [i and d that enclose the sub-areas. These equal areas or equal probabilities have been labeled in ascending order from 00000 to 99999. By this arrangement, for

any given value d the integral from to d can be calculated and the corresponding memory address is given by the first five decimal digits of the integral, disregarding the others.

In Equation 12 utilizing the values of I from Table 11, there was calculated a value d :2.07. The memory address or section corresponding to this example is exp(-)dr=0.98077 (17) V211 2 This means that the card bearing the identifier 11 of FIG. 1 is to be stored in memory section number 98077.

A significant feature regarding the treatment of the information concerning the distribution of the respective alpha-numeric characters may be noted from a consideration of the way in which a particular section address is derived. Equation 12 relates the standard deviation of the arithmetic mean to the number of identifier positions n and the corresponding values of 1. Clearly, however, this derivation of d is adaptable to identifiers having different numbers of positions with different values of t. In similar fashion, the system may be adapted to provide section addresses for memories of varying sizes. For example, the memory may easily be divided into 10,000 or 1,000 separate sections in which case the section addresses relate to the first four digits or the first three digits, respectively, of the integral of Equation 17. In a memory of 1,000 sections, for example, any item identifier having a corresponding d =2.07 would be provided with a corresponding memory address of 980. Thus the method of the invention is readily adaptable to varying situations and equipment with Whatever degree of accuracy may be desired.

FIG. 7 represents in block diagram form an arrangement of a memory address generator in accordance with the invention. The portion enclosed by the dashed line corresponds to the memory address generator 23 of FIG. 2. In FIG. 7 the tabulated information 70 is presented to a rank correlator 71, a function generator 77, and a t value storage unit 72 so that these stages may be set in accordance with the frequency distribution of the particular tabulated information as described above. When a particular memory address is to be generated, an item identifier 11 is applied to the memory address generator 23 where it is stored in a'search register 73 and is also applied to the timing circuits 74 to initiate operation of the memory address generator.

Thereafter the indexing operation begins. The contents of the search register 73 are read out serially by character and applied to the t value storage unit 72 and also to the rank correlator 71 which sends a signal representing a corresponding assigned rank to the 1 value storage unit 72. Thus, there is present in the I value storage unit 72 simultaneously information with respect to the identification of a particular character and its corresponding rank as established by the frequency distributions of the tabulated information 70. As the contents of the search register 73 are read out, the output of the 1 value storage unit 72 is applied to an adder stage 74 which provides a summation of all the respective r values corresponding to the particular alpha-numeric characters making up the item identifier 11. The summation output from the adder 75 is then applied as an input signal to the multiplier 78 for multiplication by the function supplied by the stage 77 which was previously set in accordance with the tabulated information 70. The output of the multiplier stage 78 then corresponds to the standard deviation of the mean of the respective r values as developed in Equation 12 above, and is applied as a control for an integrating amplifier 80 in order to serve as the upper limit of the integrating function of Equation 17.

As has been described above, the area under the Gaus- 2 ex ).zr:=0.0000000 N2. -00 2 Thus it can be seen that the integration from a value of 6 is undiscernible from the integration from a value of -00, insofar as the present situation is concerned.

In addition to controlling the readout of information from the search register 73, the timing circuits 74 supply a variable of integration for the integrating amplifiers and 81, which variable is designated x in FIG. 7. A

is supplied as a second input to the integrating amplifier 80. The output of this amplifier then, which is fydx, is directed to a multiplying stage 84 and is also fed back through an inverter 82 which supplies the multiplication by l to become the second input to the integrating amplifier 81. In the stage 81 an integration is performed corresponding to -fxd(fydx), so that the output of the stage 81 becomes equal to A stage 83 supplies a constant signal corresponding to the value which is applied to the multiplying stage 84 to control the multiplication of the input to the stage 84 by Thus, the function fydx, which is in reality in the stage 84 to become a voltage value at the output thereof corresponding to the desired memory address.

it will be understood that the rank correlator 71, the function generator 77 and the 2 value storage unit 72 of FIG. 7 may be arranged to operate automatically in respouse to the tabulated information 70 which is fed into the memory address generator 23 so as to order the alphanumeric characters, determine and set the r values in accordance with the frequency distribution of the information. More commonly, however, the tabulated information will be statistically analyzed by the customer before it is presented for storage in the computer memory, so that the rank correlation, the number of identifier positions, and the corresponding r values relating to the frequency distribution of the information are established by the customer. In such a case, the rank correlator 71, the generator 77, and the 1 value storage unit 72 are arranged to be adjustable so that they may be set to the appropriate values by the customer.

FIG. 8 represents schematically one specific arrangement for the t value storage unit 72 which is arranged to be adjustable in accordance with settings selected by an operator. In FIG. 8 a plurality of digital encoder is multiplied by switches 85 are shown connected between a terminal 88 and a plurality of output leads. Each of the digital encoder switches 85 is connected in series with an individually associated switch 87, represented as a pair of relay contacts controllable by a solenoid 86. Each switch 87 is given a particular rank designation from 1 to 36. In operation each digital encoder switch S5 is set in accordance with the appropriate 2 value for the corresponding rank as determined from the tabulated information. Thus, whenever the solenoid 86 for a particular rank is energized the associated switch S7 closes and presents at the output of the circuit of FIG. 8 a coded electrical signal which corresponds to the t value setting of the as sociated encoder switch 85. The numbers at the right hand side of FIG. 8 represent a typical set of r values which may be developed by this arrangement.

FIG. 9 depicts an arrangement for use in the rank correlator 71 of FIG. 7 by which an operator may designate the rank of the respective alpha-numeric characters. in FIG. 9 a plug board 91 is shown having a plurality of opposed terminals 92 and 93. The terminals 92 are designated with the respective alpha-numeric characters available for use in the item identifiers, while the terminals 93 are designated by a rank number from 1 to 36. A separate plug board 91 is provided for each position of the item identifier so that the rank correlation for each identifier position may be readily changed by the operator, simply by the substitution of a different plug board. The plug board 91 is wired by the operator by providing the proper connection between the appropriate pairs of the opposed sets of terminals 92 and 93 in accordance with the frequency distribution of the tabulated information. Thus in the arrangement shown in FIG. 7 when the search register 73 energizes a particular alpha-numeric character terminal 92. in accordance with the alpha-numeric character occurring in the panticular identifier position being read out, the associated rank terminal 93 is thereupon energized. As a result, circuit connections (not shown) energize the corresponding solenoid 86 of the circuit of FIG. 8 so as to pass to the adder 75 a signal corresponding to the alpha-numeric character under consideration. For example, if in FIG. 9 the terminal 92 designated H is energized, a voltage is passed to the terminal 93 representing the rank 4. From the rank 4 terminal the voltage is directed to the solenoid 86 of FIG. 8 corresponding to rank 4, thus causing it to operate the associated switch 87 and apply to the output of the circuit of FIG. 8 a coded signal having a numerical value determined by the setting of the appropriate digital encoder switch 85. In the example given, this signal corresponds to the 2 value of -1.04537.

The adder 75, multipliers 78 and 84 and the integrating amplifiers 80 and 81 in FIG. 7 may advantageously comprise digital differential analyzer circuits such as are known in the art. Following digital differential analyzer techniques, analog methods are used in digital fashion and it is possible to achieve five-digit accuracy in such operations. Thus, the use of digital differential analyzers in the generation of the normal cumulative distribution function and the integration over the Gaussian curve materially simplifies the structure needed to attain the desired precision while augmenting the performance of the systern of; the invention. An additional advantage accrues from the fact that digital differential analyzers provide an output signal in digital form, thus eliminating the need for an analogato-digital converter which would otherwise be needed if the memory address were generated by means of analog operational amplifiers. A particular type of digital differential analyzer circuit which may be employed in the above-mentioned stages is described in a publication entitled The Design of the Bendix Digital Differential Analyzer, by M. Palevsky, appearing in The Proceedings of the IRE, October 1953, pages 1352 ff. The search register 73 and the timing circuits stage 74 comprise circuitry which is well known to those skilled 20 in the art. It is therefore considered unnecessary to furnish the details of the circuits here.

In the arrangement of the invention depicted in FIG. 7, it is implied that the memory address generator system will be operated in accordance with the description of the transformation process set forth above. By this, it is meant that a standardized cumulative distribution curve for each of the different identifier positions is obtained, so that in general the rank correlator 71 must supply correlation with thirty-six ranks for each of twenty-five identifier positions; and in addition the 1 value storage unit 72 must have provision for 25x36=900 different Ways for the operator to set the t values for a particular identifier set. While this is rigorous from a purely mathematical point of view, it is possible to depart slightly from pure theory in order to provide a somewhat more practical system. As a suitable compromise, the number of curves which are depended upon to provide the settings of the rank correlato-r 71, the generator 77, and the t value storage unit 72 may be substantially reduced. For example, if it is desired to use three curves, instead of twenty-five, each one of the three may be a composite which is derived from particular ones of the twenty-five identifier position curves. A composite curve is prepared by taking the averages of the midpoint cumulative frequencies corresponding to respective ranks. Thus, for example, suppose that identifier positions 00 through 09 are to be combined in one composite curve from the statistical tables prepared in the manner illustrated in connection with Table I. All of the midpoint cumulative frequencies corresponding to rank 1 for the positions 00 through 09 are added and the result is divided by 10 to arrive at an average midpoint cumulative frequency for rank 1. The same thing is done for rank 2 and so on through all of the ranks in the table. These averaged values are then used as the basis for locating a corresponding value of I from a statistical table of cumulative distribution function. Similar operations are performed in connection with the remaining identifier positions in order to derive the remaining composite curves. The composite curves thus derived are then combined in accordance with the principles of the Addition Theorem, as described above in the development of Equation 12, to arrive at the desired value of standard deviation, d The advantage of performing this process to derive the composite curves is that the number of t values needed for the value storage unit 72 is materially reduced without significant sacrifice in the accuracy obtainable in the practice of the invention.

in the circuits set forth in FIG. 8, the digital encoding switches 85, front which the corresponding 1 values are derived, have been shown in a rudimentary form in order to simplify the understanding of the arrangement. To provide the requisite accuracy of the various t values to five or six decimal places. each digital encoding switch may comprise a plurality of decade switches as shown in FIG. 10.

In FIG. 10 a single digital encoder switch 85 is shown comprising a plurality of decade switches a-110f, each comprising a ten-position switch which functions to connect the input terminal 38 to a selected one of ten output leads for each decade switch whenever the solenoid 86 associated therewith closes the contacts 87. Each of the decade switches 110a-110f corresponds to a significant digit of a multiple digit number so that the appearance of signals on selected ones of the output leads provides a coded electrical signal having a numerical value determined by the settings of the digital encoder switches 110al1l)f. Thus, by setting the digital encoder switches 1100-110f to a selected 1 value, coded electrical signals are generated corresponding thereto. Since the desired 1 values may be either positive or negative, the digital encoder switch 85 may also include a single pole double throw switch 11 which selectively provides an 

1. A SYSTEM FOR AUTOMATICALLY STORING INFORMATION WHICH IS INDIVIDUALLY DESIGNATED BY SPECIFIC CODED IDENTIFIERS COMPRISING A MEMORY UNIT HAVING A PLURALITY OF DISCRETE SECTIONS THEREIN EACH BEARING AN INDIVIDUAL MEMORY ADDRESS, A PLURALITY OF INFORMATION ITEMS HAVING INDIVIDUAL IDENTIFIERS, A MEMORY ADDRESS GENERATOR FOR PRODUCING A PARTICULAR MEMORY ADDRESS CORRESPONDING TO AN INDIVIDUAL ITEM IDENTIFIER IN ACCORDANCE WITH THE STATISTICAL DISTRIBUTION OF THE IDENTIFIER CHARACTERS WITHIN THE PLURALITY OF INFORMATION ITEMS TO BE STORED IN THE MEMORY UNIT, MEANS FOR APPLYING AN INDIVIDUAL ITEM IDENTIFIER TO THE MEMORY ADDRESS GENERATOR, TRANSLATING MEANS FOR PASSING INFORMATION FROM A PARTICULAR INFORMATION ITEM TO THE CORRESPONDING MEMORY UNIT SECTION BEARING THE ADDRESS PROVIDED BY THE MEMORY ADDRESS GENERATOR, AND MEANS FOR RETRIEVING THE INFORMATION THUS STORED BY APPLYING A GIVEN CODED IDENTIFIER TO THE MEMORY ADDRESS GENERATOR AND READING OUT THE CORRESPONDING INFORMATION FROM THE PARTICULAR MEMORY UNIT SECTION DESIGNATED BY THE ADDRESS PROVIDED BY THE MEMORY ADDRESS GENERATOR. 